The revenue R received by a company selling x pairs of sungl

The revenue R received by a company selling x pairs of sunglasses per week is given by the function R(x) -0.1x^2=80x. (a) Find the values of R(13) and R(25). (b) How many pairs of sunglasses must be sold in order for the revenue to be $7000 per week? (c) How many pairs of sunglasses must be sold in order for revenue to be 16,000 per week? please explain! thank you

Solution

R(x) -0.1x^2=80x

R(x) = 80x +0.1x^2

a) R (13) plug x= 13: R(13) = 80*13 +0.1*13^2 = $1056.9

R(25) plug x= 25 ; R(25) = 80*25 +0.1*25^2 = $ 2062.5

b) revenue to be $7000 per week:

7000 = 80x +0.1x^2

0.1x^2 +80x -7000 =0

solve the quadratic using quadratice formula : ax^2 +bx +c =0

x = (-a +/-sqrt(b^2 -4ac) )/2a

= (-80 +/- sqrt(80^2 +7000*0.1*4) )0.2

Neglect the -ve root:

x= 79.58 = 79 suglasses or 80 sunglasses

c) revenue to be $16,000 per week

0.1x^2 +80x -16000 =0

solve the quadratic using quadratice formula : ax^2 +bx +c =0

x = (-a +/-sqrt(b^2 -4ac) )/2a

= ( -80 +/- sqrt(80^2 +4*0.1*16000) )/0.2

x = 165.68 = 166 or 165 sunglasses

depending upon if you want to round off